K$^+$-nucleon interaction

The Born approximation to the quark-gluon-exchange mechanism for K$^+$N scattering is used as a starting point to generate a potential for this system. The valence quark wave function of the nucleon is generalized from a single Gaussian to a sum of Gaussians in order to have a more flexible representation than previous work. We obtain a potential derived from a valence density given by lattice calculations. By comparing with a recent amplitude analysis it is found that the strength of the quark-gluon based potential needs to be increased by a factor of order 2-4 relative to the normalization given by more traditional values of the governing parameters. The method is used to estimate the change in effective K$^+$N amplitudes which would result from changes in the valence quark distributions or strength of the interaction which might arise from nuclear medium effects in K$^+$ scattering from nuclei.